A circular pond is modeled by the equipment x^2+y^2=225. A bridge over the pond is modeled by a segment of the equation x-7y=-75. What are the coordinates of the points where the bridge meets the edge of the pond?

Question

anonymous · Answer

Solve simultaneously.

anonymous · Answer

I don't know what you mean

anonymous · Answer

For example $$x=7y-75$$ then $$(7y-75)^2+y^2=225$$ finally solve for the two values of y and substitute in the linear equation to get the corresponding x values

anonymous · Answer

the solutions should be (-12,9) and (9,12)

anonymous · Answer

thanks

anonymous · Answer

ok s I got till -50y^2-1050y+5400=0
But where do I go from there?

anonymous · Answer

Divide everything by -50

anonymous · Answer

Correction$$50*y^2-1050*y+5400$$

anonymous · Answer

$$y^2-21y+108=0$$
implies$$(y-9)(y-12)=0$$

anonymous · Answer

How, did you factor or something?

anonymous · Answer

Yeah

anonymous · Answer

ok, also why did you divide by 50. Is it because it was in front of y^2

anonymous · Answer

We dont need the 50 since $$50(y^2-21y+108)=0$$ iff $$y^2-21y+108=0$$ by the zero product property

anonymous · Answer

oh ok, I get it. thanks